Question

9. The force of attraction between
two bodies at a separation is 25N.
The force of attraction between
them when the separation is doubled
is *​

Answer 1

Given that,

The force of attraction between two bodies ( Gravitational force ) at a separation is 25 N.

Let the separation be d meters and mass of the two bodies be m₁ and m₂ respectively.

According to the question,

⇒ F₁ = 25 N

⇒ F₁ = Gm₁m₂ / d² = 25 N ...(1)

Also,

We need to find the force of attraction when the distance between them is doubled.

⇒ F₂ = Gm₁m₂ / (2d)²

⇒ F₂ = Gm₁m₂ / 4d²

⇒ F₂ = 1/4 [ Gm₁m₂ / d² ]

⇒ F₂ = F₁ / 4

⇒ F₂ = 25 / 4 [ from (1) ]

⇒ F₂ = 6.25 N

Hence, The force of attraction between them would become 6.25 N.

Some Information :-

☛ Gravitational force is the force of attraction between two bodies of mass m₁ and m₂ respectively at a distance of d meters.

Magnitude = Gm₁m₂ / d²

G = Gravitational constant

= 6.67 × 10⁻¹¹ Nm² / Kg²

From the Equation, We get to know that:

• Gravitational force between two bodies is inversely proportional to the distance between them. Which means when the distance between them is doubled, the force of gravitation between them is reduced to half.